It is well known that the received signal may be affected by the so-called Doppler effect in the wireless mobile communication, and a Doppler frequency shift may be produced with respect to the transmittal signal. The size and the feature of the frequency shift may be determined by the relative motion between the transmitter and the receiver, and the environment of the signal transmission. However, phase rotation, even the phase reversion, may occur on the received wireless communication transmitting signal. Therefore, the influence of those factors should be fully considered while detecting the signal. Otherwise, the performance of the signal detection will inevitably be affected.
If the complex discrete signal transmitted is assumed as X(k) (k=0 . . . L−1), then the received discrete signal after sampling will be:Y(k)=a(k)*X(k)*ejφ(k)+n(k), (k=0 . . . L−1)  (1)
wherein, a(k) is an attenuation factor after passing through the channel, φ(k) is a phase rotation angle after the signal passing through the channel, n(k) is an additive noise, and k represents the indices of the discrete signal, under the condition of transmitting the data and sampling the signal at a constant rate. It can also be considered as a representation of the indices of the time. The total number of the signal samples for performing the signal detection is L.
Several typical signal detection methods of the related art are shown as below:
1. Coherent signal detection method, in which, the signal will be coherent accumulated directly in a range with a length of L. That is, the transmitted signal and the received signal will be multiplied by conjugation, and the multiplied result will be accumulated in the range with the length L. Then the summing result obtained finally is calculated for the square of the mode, which is used as a decision statistic of the coherent detection. The decision statistic is represented by the following equation:                               Z          coherent                =                                                                        ∑                                  k                  =                  0                                                  L                  -                  1                                            ⁢                                                           ⁢                                                Y                  ⁡                                      (                    k                    )                                                  *                                                      X                    *                                    ⁡                                      (                    k                    )                                                                                            2                                    (        2        )            
The equation 2 will be substituted by the equation 1 of the received signal, obtaining:                               Z          coherent                =                                                                                          ∑                                      k                    =                    0                                                        L                    -                    1                                                  ⁢                                  [                                      a                    ⁢                                                                                   ⁢                                          (                      k                      )                                        *                                          X                      ⁡                                              (                        k                        )                                                              *                                                                  X                        *                                            ⁡                                              (                        k                        )                                                              *                                          q                                              j                        ⁢                                                                                                   ⁢                                                  ϕ                          ⁡                                                      (                            k                            )                                                                                                                                ]                                            +              n                                            2                                    (        3        )            
Where,       n    =                  ∑                  k          =          0                          L          -          1                    ⁢                                    X            *                    ⁡                      (            k            )                          *                  n          ⁡                      (            k            )                                ,      X    *          (      k      )      is a complex conjugate signal of X(k).
A good detection result can only be obtained by using such detection method when the phase of the received signal varies not so significant within the length L. It is difficult to achieve a phase of the received signal that does not vary significantly within the length L, under certain communication environments.
2. Non-coherent detection method: The fundamental idea of this detection method is to divide the signal of L samples used to detect the signal into the segments with equal space Nnoncoh (Nnoncoh>1). The length of each segment is L/Nnoncoh=Snoncoh. The coherent accumulating sum T(m) will be calculated for each length of Snoncoh, that is:                                           T            ⁡                          (              m              )                                =                                    ∑                              k                =                0                                                              S                  noncoh                                -                1                                      ⁢                          [                                                Y                  ⁡                                      (                                                                  m                        *                                                  S                          noncoh                                                                    +                      k                                        )                                                  *                X                *                                  (                                                            m                      *                                              S                        noncoh                                                              +                    k                                    )                                            ]                                      ,                                  ⁢                  m          =                                    0              ⁢                                                           ⁢              …              ⁢                                                           ⁢                              N                noncoh                                      -            1                                              (        4        )            
The coherent result of each segment is T(m), and there are Nnoncoh total data, then the non-coherent accumulating will be performed again. The equation for calculating the decision statistic will be obtain as follows:                               Z          ⁡                      (            k            )                          =                              ∑                          m              =              0                                                      N                noncoh                            -              1                                ⁢                                                                  T                ⁡                                  (                  m                  )                                                                    2                                              (        5        )            
Substitute the equation 1 and 4 into 5, then obtain:                               Z          ⁡                      (            k            )                          =                              ∑                          m              =              0                                                      N                noncoh                            -              1                                ⁢                                                                ∑                                  k                  =                  0                                                                      S                    noncoh                                    -                  1                                            ⁢                              [                                                      a                    ⁡                                          (                                                                        m                          *                                                      S                            noncoh                                                                          +                        k                                            )                                                        *                                      X                    ⁡                                          (                                                                        m                          *                                                      S                            noncoh                                                                          +                        k                                            )                                                        ⁢                                      *                    2                                                                                                          (        6        )                                                                                                                 ⁢                              X                *                                  (                                                            m                      *                                              S                        noncoh                                                              +                    k                                    )                                *                                  ⅇ                                      jϕ                    ⁡                                          (                                                                        m                          *                                                      S                            noncoh                                                                          +                        k                                            )                                                                                  ]                        +                                          n                m                            ⁡                              (                m                )                                                              2                                         
Where,             n      m        ⁡          (      m      )        =            ∑              k        =        0                              S          noncoh                -        1              ⁢                  [                                            X              *                        ⁡                          (                                                m                  *                                      S                    noncoh                                                  +                k                            )                                *                      n            ⁡                          (                                                m                  *                                      S                    noncoh                                                  +                k                            )                                      ]            .      
To achieve better performance by this detection method, it is required that the phase of the received signal remain constant within the signal length of Snoncoh. However, even when the phase of the received signal may be maintained constant within L (I>Snoncoh), then the detection performance loss of the non-coherent detection method will be smaller than the gain obtained from suppressing the phase rotation. In general, it is worse than the coherent detection method of Method 1.
3. Differential detection method: The fundamental idea of this method is also to divide L samples into segments with equal spaces Ndiff (Ndiff>1), where the length of each segment is L/Ndiff=Sdiff, by using the coherent accumulating method for each length of Sdiff. Ndiff coherent accumulating values will be obtained:                               Q          ⁡                      (            m            )                          =                                            ∑                              k                =                0                                                              S                  diff                                -                1                                      ⁢                                          [                                                      Y                    ⁡                                          (                                                                        m                          *                                                      S                            diff                                                                          +                        k                                            )                                                        *                  X                  *                                      (                                                                  m                        *                                                  S                          diff                                                                    +                      k                                        )                                                  ⁢                                                                   ]                            ⁢                                                           ⁢              m                                =                                    0              ⁢                                                           ⁢              …              ⁢                                                           ⁢                              N                diff                                      -            1                                              (        7        )            
The coherent result Q(m) of two consecutive segments will be conjugately multiplied by each other, resulting in total of Ndiff−1 multiplications, then adding the real part of Ndiff−1 mutiplications, and obtaining the following equation for calculating the decision statistic:                     Z        =                              ∑                          m              =              0                                                      N                diff                            -              2                                ⁢                      Re            ⁢                          {                                                Q                  ⁡                                      (                    m                    )                                                  *                Q                *                                  (                                      m                    +                    1                                    )                                            }                                                          (        8        )            
Substitute the equation 1 and 7 into 8, and expend it to obtain:                                           z            =                                          ∑                                  m                  =                  0                                                                      N                    diff                                    -                  2                                            ⁢                              Re                ⁢                                  {                                                                                    ∑                                                  k                          =                          0                                                                                                      S                            diff                                                    -                          1                                                                    ⁢                                              [                                                                              a                            ⁡                                                          (                                                                                                m                                  *                                                                      S                                    diff                                                                                                  +                                k                                                            )                                                                                *                                                      X                            ⁡                                                          (                                                                                                m                                  *                                                                      S                                    diff                                                                                                  +                                k                                                            )                                                                                *                          X                          *                                                      (                                                                                          m                                *                                                                  S                                  diff                                                                                            +                              k                                                        )                                                    *                                                      ⅇ                                                          jϕ                              ⁡                                                              (                                                                  m                                  *                                                                      S                                    diff                                                                          +                                      k                                                                                                                                      )                                                                                                                                    ]                                                              +                                                                  n                        m                                            ⁢                      m                                                        )                                                              )                *                  (                                                    ∑                                  k                  =                  0                                                                      S                    diff                                    -                  1                                            ⁢                              [                                                      a                    ⁡                                          (                                                                                                    (                                                          m                              +                              1                                                        )                                                    *                                                      S                            diff                                                                          +                        k                                            )                                                        *                                      X                    ⁡                                          (                                                                                                    (                                                          m                              +                              1                                                        )                                                    *                                                      S                            diff                                                                          +                        k                                            )                                                        *                  X                  *                                      (                                                                                            (                                                      m                            +                            1                                                    )                                                *                                                  S                                                      diff                            ⁢                                                                                                                                                                                     +                      k                                        )                                    *                                      ⅇ                                          jϕ                      ⁡                                              (                                                                              (                                                          m                              +                              1                                                        )                                                    *                                                      S                            diff                                                          +                              k                                                                                                      )                                                                                            ]                                      +                                          n                m                *                            ⁡                              (                                  m                  +                  1                                )                                              )                                    (        9        )            
Where,             n      m        ⁡          (      m      )        =            ∑              k        =        0                              S          diff                -        1              ⁢          [                        n          ⁡                      (                                          m                *                                  S                  diff                                            +              k                        )                          *        X        *                  (                                    m              *                              S                diff                                      +            k                    )                    ]      
Same as method 2, the application condition of the differential detection method can be satisfied only if the phase of the received signal maintains substantially constant within Sdiff. Nevertheless this method has similar application conditions as Method 1 (the phase of the received signal maintains substantially constant within the length L). The detection performance loss of the differential detection method itself is also smaller than the gain obtained from suppressing the phase rotation. In general, it is worse than the detection performance of the coherent detection method of Method 1.
4. Combination detection method: This method of the combination of the above three methods. The range of Doppler frequency shift may be detected (or specified) by certain methods. In the case of high Doppler frequency shift, the non-coherent or differential detection method may be used; while in the case of low Doppler frequency shift, the coherent detection method can be used. The implementation of this method is rather difficult, and the optimum detection performance can not be obtained yet.
By comparing in general:
Method 1 is established on the basis of assuming that the phase of the signal maintains substantially constant within a range of the length L, in the case of low frequency shift (including Doppler frequency shift and system frequency shift, the same below). This condition can be satisfied substantially (according to the chip rate and the signal length L, the same below), and an excellent detection effect can be reached; but in the case of large frequency shift, this assumption may not be established. Within the length L, the signal phase may be change greatly even the phase reverse may occur. This may cause the coherent results to cancel each other out. Thereby, the detection performance decreases rapidly, even non signal can be detected.
The application condition of Method 2 will relax to: keeping the signal phase within the length Snoncoh (Snoncoh<L), substantially constant, so that in the case of a higher frequency shift, the signal phase may not be changed greatly when it is within Snoncoh (it should be noted, that Snoncoh=L/Nnoncoh<L), and the performance degradation appearing in Method 1 will no longer occur. In this situation, the performance will be better than that of Method 1. However, in the case of a low frequency shift, Method 1 also has the condition of maintaining the signal phase as a constant within the coherent length L. At this time, comparing the non-coherent of Method 2 with Method 1, a certain performance loss may exist.
Method 3 is as same as that analyzed in Method 2, in the case of higher frequency shift, though the differential detection method can obtain a better detection performance than that of Method 1. However, in the case of low frequency shift, the performance loss will be larger than that of Method 1.
Although a better performance can be achieved by using Method 4 in the case of a variety of Doppler frequency shift, it is complicated by using the method of the protocol limitation. By using the detection method, the Doppler frequency shift estimate module is required, so that, it is difficult to ensure accuracy.